Solve the problem
How many 4-letter passwords can be formed from the letters P,A,Y,M,E,N,T if no repetition of letters is allowed
There are 7 letters to choose from, and we want to form a 4-letter password without repetition.
To solve this problem, we will use the concept of permutations.
The number of permutations of n objects taken r at a time is given by the formula: P(n, r) = n! / (n - r)!
In this case, we want to find P(7, 4) as we have 7 letters and want to choose 4 of them.
P(7, 4) = 7! / (7 - 4)!
= 7! / 3!
= (7 * 6 * 5 * 4 * 3!) / 3!
= 7 * 6 * 5 * 4
= 840
So, there are 840 different 4-letter passwords that can be formed from the letters P, A, Y, M, E, N, and T without repetition.